Performance Evaluation of Solid Oxide Fuel Cell Engines Integrated With Single/ Dual...

So-Ryeok Oh1e-mail: [email protected]

Jing Sune-mail: [email protected]

Naval Architecture and Marine Engineering,

University of Michigan,

Ann Arbor, MI 48109

Herb Dobbs

Joel King

U.S. Army TARDEC,

6501 E. 11 Mile Road,

Warren, MI 48397-5000

Performance Evaluation ofSolid Oxide Fuel Cell EnginesIntegrated With Single/Dual-Spool TurbochargersThis study investigates the performance and operating characteristics of 5kW-class solidoxide fuel cell and gas turbine (SOFC/GT) hybrid systems for two different configura-tions, namely single- and dual- spool gas turbines. Both single and dual spool turbo-chargers are widely used in the gas turbine industry. Even though their operation isbased on the same physical principles, their performance characteristics and operationparameters vary considerably due to different designs. The implications of the differenceson the performance of the hybrid SOFC/GT have not been discussed in literature, andwill be the topic of this paper. Operating envelops of single and dual shaft systems areidentified and compared. Performance in terms of system efficiency and load following isanalyzed. Sensitivities of key variables such as power, SOFC temperature, and GT shaftspeed to the control inputs (namely, fuel flow, SOFC current, generator load) are charac-terized, all in an attempt to gain insights on the design implication for the single and dualshaft SOFC/GT systems. Dynamic analysis are also performed for part load operationand load transitions, which shed lights for the development of safe and optimal controlstrategies. [DOI: 10.1115/1.4004471]

1 Introduction

Solid oxide fuel cells (SOFC), which operate at elevated tem-peratures (�800 �C), are particularly well suited to combine witha gas turbine (GT) as the bottoming cycle in a hybrid SOFC-GTconfiguration. By integrating the two power plants with comple-mentary characteristics, the efficiency of such a system can poten-tially exceed 60% and even approach 70% for future optimizeddesigns [1–4].

Various layouts for hybrid SOFC/GT plant have been proposedin the literature. Most of them include combinations of SOFCstacks, heat exchangers, compressor, gas turbines, prereformer,and combustors in different arrangements [2,3]. Most of theSOFC/GT designs replace the gas turbine combustor directly withthe fuel cell stack, resulting in the stack being pressurized at theoperating pressure of the gas turbine [5]. Other designs, such asthe atmospheric SOFC/GT system proposed in Ref. [6] can bealso found in literature. It has been shown that the wide range ofoperation can be supported by burning residue and supplementaryfuel in the afterburner. Both simulation and experimental studiesshow that the steady state efficiency increases substantially for theintegrated SOFC/GT systems, compared to their stand-aloneSOFC or GT modules [3]. Achieving high efficiency of theSOFC/GT system without compromising system safety and reli-ability represents a key challenge for control development [9].Modeling efforts have been reported by various group aimed atfacilitating control design and optimization [8].

This paper, built on our previous work [10] which was focusedon developing a fast load following scheme, presents a compara-tive study about the performance capability of two distinct SOFC/GT designs shown in Fig. 1.

One is a single-shaft design with the compressor and turbinemounted on the same shaft as the power generator. Another is a

dual-shaft design with two turbines, namely one drives a compres-sor and another is a free power turbine driving a generator. Whilethe single- and dual-shaft turbine configurations have been widelyemployed for SOFC/GT hybrid systems study, to the best of ourknowledge, the effects of turbine connection mechanisms on theSOFC/GT operation have not been reported in the open literature.In particular, this paper addresses the following topics: First, theperformance capability of the two different SOFC/GT designs iscompared in terms of a part-load envelope, system efficiency, andSOFC temperature level. Second, the sensitivity of crucial systemparameters on the control variables, namely the fuel flow, SOFCcurrent density, and generator loads, is analyzed and admissibleranges for control variables and advantageous load operationpoints are identified through model based analysis. Furthermore,applying the derived operation points, the shutdown behavior ofthe SOFC/GT cycles during load changes is explored through aregion of attraction analysis for both single and dual shaft system.

The remainder of this paper is organized as follows: in the nextsection the system operation principles are presented. SOFC andthe gas turbine models are described in Secs. 3 and 4, respectively.Performance evaluations in the steady state and transient are pre-sented in Secs. 5 and 6, respectively, followed by the conclusions.

2 System Operation Principles

The hybrid SOFC/GT system analyzed in this work is intendedas an auxiliary power unit (APU) for military and commercial ve-hicle applications. For example, this unit can be employed in acommercial vehicle to avoid idling of the main engine for powerproduction during stops to improve efficiency. Additionally, it canbe used to recharge batteries in the field as well as act as genera-tors. The system is designed to have a rated power of around5kW. The utility of a dual-shaft gas turbine, shown in Fig. 1(b), isexplored in comparison with its single shaft counterpart in achiev-ing efficient steady state operation and smooth transient responsefor a highly coupled SOFC/GT system. The key system compo-nents include an SOFC stack, a compressor (C), a catalytic burner(CB) as the after-burner, turbines (T) which drives a generator

1Corresponding author.Contributed by the Advanced Energy Systems Division of ASME for publication

in the JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY. Manuscript received April26, 2011; final manuscript received May 8, 2011; published online October 5, 2011.Editor: Nigel M. Sammes.

Journal of Fuel Cell Science and Technology DECEMBER 2011, Vol. 8 / 061020-1CopyrightVC 2011 by ASME

Downloaded 02 Oct 2012 to 141.212.93.52. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

(GEN). Other components, such as the reformer and the heatexchangers, are not included in this work in order to focus on thecoupling dynamics between the SOFC and the GT.

The description of the general working principles of the SOFC/GT systems can be found in Ref. [9]. For most of the SOFC/GTsystems, the air to the SOFC is supplied to the cathode side by acompressor, while fuel is fed to the anode side. The exhaust fromthe SOFC outlet passes through the CB where the unused fuel isburned to increase the temperature and pressure of the flow. Thehigh temperature and high pressure flow from the CB then powersthe turbine, thereby providing a mechanism to recuperate theexhaust energy. In the single-shaft design (Fig. 1(a)) the turbinedrives both the compressor and the generator through a mechani-cal shaft; the former delivers the air needed for the SOFC stackoperation and the latter provides additional electrical power forthe system. The net power output is the sum of the electric powerfrom the SOFC and the generator. On the other hand, in the split-shaft design (Fig. 1(b)) there are two turbines. One is a gasifierturbine driving a compressor and another is a free power turbinedriving a generator. Since these two turbines have no mechanicalcoupling, the design can offer better flexibility of operation for thecompressor and the power turbine. In the sequel, the modeling ofthe plant components is explained.

3 SOFC Model Description

SOFC is the key component of the system. In this work, thetubular type SOFC, used in most of SOFC/GT studies due to itsadvantages in terms of the thermal expansion and gas sealing, isconsidered and its dynamic model is established.

In a tubular design, air is supplied to the inside of the tube andfuel to the outside (see Fig. 2). Air enters the feed tube at the bot-tom and travels to the closed end of the cell at the top. Fuel enterson the outside at the closed end. The air and fuel both flow alongthe cell in the same direction from the closed end toward the openend. This is known as a co-flow configuration.

3.1 Tubular SOFC Model. Our modeling approach takesinto account the trade-off between acceptable computational loadand sufficient model accuracy. The following modeling strategieshave been implemented to reduce the complexity of the resultingmodel without significant compromise on the accuracy: (1) Theanode, cathode, and electrolyte are treated as one single entity.Based on the physical structure of the SOFC, five temperaturelayers were defined, namely the temperatures for the fuel bulkflow, air bulk flow, positive electrode-electrolyte-negative elec-trode assembly (PEN), injector, injector air. (2) The fuel is amixture of six species, consisting of methane(CH4), carbon mon-oxide(CO), carbon dioxide(CO2), hydrogen(H2), steam(H2O) andnitrogen(N2), where the concentration of each species can be var-

ied to reflect different prereforming results. (3) The SOFC can betreated as a distributed parameter system in order to capture thespatial distribution along the flow field for variables such as tem-perature, species concentration, and current density. The govern-ing equations are described using discretization technique [11]. Inthis modeling effort, the cell is divided into n axial sections (seeFig. 2) and each section is considered as a lumped parameter sub-system.

3.1.1 Electrochemical Model. The operating voltage of onediscretization unit of the cell can be calculated as follows:

Uj ¼ UjOCV � ðgjohm þ gjact þ gjconÞ; j ¼ 1; 2;…; n; (1)

where j is the index of discretization units, as shown in Fig. 2.Uj

OCV is the open circuit voltage in the jth unit. For simplicity, thesuperscript j will be omitted in the rest of the presentation. Theopen circuit voltage can be determined by the Nernst Equations asfollows:

UOCV ¼ E0 �~RTPEN2F

lnpH2O

pH2p0:5O2

(2)

Fig. 1 SOFC/GT Hybrid schematic: single-shaft (a) and dual-shaft (b)

Fig. 2 Finite volume discretization for a tubular SOFC

061020-2 / Vol. 8, DECEMBER 2011 Transactions of the ASME


with E0¼ 1.2723� 2.7645� 10-4TPEN [11], where TPEN is thetemperature of the PEN structure, and pH2O

, pH2, and pO2

are thepartial pressures of H2O, H2, and O2, respectively. The last threeterms in Ref. [1] represents various potential losses: The activa-tion loss, nact, is due to the energy barriers to be overcome in orderfor the electrochemical reaction to occur, and can be characterizedby the Butler-Volmer equation. The concentration loss, gcon,reflects the overpotential due to the species diffusion between thereaction site and the bulk flow in gas channels, and gohm is theohmic loss due to the electrical and ionic resistance along the pathof the current in the fuel cell. The ohmic, activation and concen-tration polarization are calculated according to the procedure dis-cussed in Ref. [11].

3.1.2 Mass Balances. For the mass balance in the fuel chan-nel, the chemical species considered are CH4, H2O, CO, CO2, H2,and N2, while for the air channel the chemical species are O2 andN2. Table 1 presents the fuel and air channel mass balance equa-tions. In the fuel channel, three reactions are taken into account:methane steam reforming (SR), water gas-shift (WGS), andhydrogen electrochemical oxidation (Ox). In the air channel, onlythe reduction reaction of O2 to O2� ions is considered (Red). Ta-ble 2 lists all these reactions. According to Faraday’s law, therates of Ox and Red reactions are related to the current density asfollows:

rOx ¼ rRed ¼ i

2F(3)

The SR reaction is slow and highly endothermic, while theWGS is fast and weakly exothermic. Thus, the entire reformingprocess is dominated by the endothermic SR reaction that requiresthe heat generated by the electrochemical reaction. In this study,the model proposed by Ref. [11] is adopted for the reaction rate ofthe fuel reforming reaction, namely:

rSR ¼ 0:04274 � pCH4� exp � ESR

~RTf

!(4)

with ESR¼ 82 kJmol�1 and all the CO is assumed to be convertedthrough the shift reaction, considered to be at equilibrium [12].The formula given in Ref. [12] is used to account for this effect:

rWGS ¼ kWGS � pCO � 1� pCO2pH2

pCOpH2OKeq;WGS

� �(5)

where kWGS¼ 0.01 in this model and Keq,WGS is the equilibriumconstant with Keq,WGS¼ exp(4276/Tf – 3.961) where Tf is the tem-perature of the fuel channel.

3.1.3 Energy Balances. The temperatures in five layers, i.e.,the fuel/air bulk flow (Tf/Ta), PEN structure (TPEN), the feed tube/air (T1, T1a), are calculated by solving the dynamic equations ofthe energy balance in each layer. The energy balance dynamicsare listed in Table 3. Right-hand side (RHS) terms in the equationsare composed of rate of energy entering/leaving a control volumeby inflow/outflow and rate of heat added/dissipated through bothchemical reaction and heat transfer. The heat transfer processesinclude heat release due to the chemical and electrochemical reac-

tions and electrical resistances; convective heat transfer betweencell components and fuel and air gas streams; and heat conductionthrough cell components; radiation heat exchange between thePEN and an air feed tube.

3.2 Dynamic Simulation and Model Validation. A tubularSOFC model was implemented in the Matlab/Simulink environ-ment. The model predicts the various temperatures along the flowpath, the gas composition in the fuel and air channel, all the elec-trochemical-related variables (open-circuit voltage, current den-sity) as well as the cell efficiency and power output. The cellparameters, such as operating conditions and the physical propertyvalues of the cell materials and geometry, have taken from the lit-erature [11,13]. The simulations were conducted under the follow-ing conditions: the cell inlet temperature is 1000K, fuelutilization is set to 85%, and air has a stoichiometric ratio of four.Figure 3(a) shows the results of different temperature profiles forthe fuel and air channels, PEN structure, and injector, along the

Table 1 Dynamic SOFC model: mass balance equation

Fuel channel_Ci;f ¼ Nin;f � Nout;f

� �1vfþPk2 SR;WGS;Oxf g vi;krk

1df

i [ {CH4, CO2, CO, H2O, H2, N2}Air channel

_Ci;a ¼ Nin;a � Nout;a

� �1vaþPk2 Redf g vi;krk

1da

i [{O2, N2}

Table 2 Reactions considered in the model

Location Reaction Expression

Fuel channel SR CH4þH2O! COþ 3H2

WGS COþH2O! CO2þH2

Anode Ox H2þO2� ! H2Oþ 2e�

Cathode Red O.5O2þ 2e—! O2�

Table 3 Dynamic SOFC model: energy balances

Fuel channel

Xf

qfcp;f

!dTf

dt¼ qin;f � qout;f� � 1

1þ kf;PEN TPEN � Tfð Þ 1

df

þ r0x hH2O TPENð Þ � hH2Tfð Þ½ � 1

df

f 2 CH4;CO2;CO;H2O;H2;N2f gCell Air ChannelX

a

qacp;a

!dTa

dt¼ qin;a � qout;a� � 1

1þKa;PEN TPEN � Tað Þ 1

da

þ Ka;I TPEN � Tað Þ 1ha

� 0:5rRedhO2Tað Þ 1

da

i 2 O2;N2f gPEN structure

qPENCV ;PEN

dTPEN

dt¼qcond;PEN�kf;PEN TPEN�Tfð Þ 1

sPENþka;I TPEN�Tað Þ 1

sPEN

þr0x hH2Tfð Þþ0:5hO2

Tað Þ�hHO2TPENð Þ½ � 1

sPEN� iU

þ r T4I�T4

PEN

� �1=eIþ1=ePEN�1

� �1

sPEN

Injector

qIcv;IdTI

dT¼qcond;Ia � kIa;I TIa � TIð Þ 1

sI� Ka;I TPEN � Tað Þ 1

sI

� r T4I � T4

PEN

� �1=eIþ1=ePEN � 1

� �1

sI

Feed Air

XIa

qIacp;Ia

!dTIa

dt¼ qin;Ia � qout;Ia� � 1

1þ kIa;I TIa � TIð Þ 1

dIa

Ia 2 O2;N2f g

Journal of Fuel Cell Science and Technology DECEMBER 2011, Vol. 8 / 061020-3


flow axis. It can be seen that the cell temperature increases alongthe fuel and air flow directions with the maximum temperatureoccurring at the outlet. Figure 3(b) presents the mole fraction pro-files in the fuel channel stream. These illustrate the impact of thesimultaneous occurrence of the direct internal reforming reaction,the water gas shift reaction, and the oxidation of hydrogen at theanode-electrolyte interface. The consumption of hydrogen and theproduction of steam can be clearly identified along the cell lengthas the hydrogen oxidation reaction proceeds. At the exit of thefuel channel, all the methane has been fully consumed and thestream content is 33% in H2O, 4% in CO, 6% in H2, and 16% inCO2.

Figure 4 presents the cell voltage and power density as a func-tion of current density. In Fig. 4(a), the simulation results arecompared to the actual test data taken from Ref. [1] for voltage

and power output corresponding to different current density. Thiscomparison shows a good match between the simulation modeland the test data (presented in literature) as the percent errorbetween the model prediction and experimental test data is lessthan 3% over the entire current density range.

In order to combine the tubular SOFC with a gas turbinecycle, the nominal cell operation point has been selected tomatch the gas turbine system. The cell operating point is oftendesigned to be where the ohmic resistance has a dominant influ-ence. For this tubular SOFC system, this corresponds to a voltagerange of 0.6� 0.7 V. With this voltage range, an average currentdensity of 2000 A/m2 and a single cell power of 90 W have beencalculated from the cell current power profile shown in Fig. 4(b).The stack was chosen to have 60 cells in order to produce a ratedpower of 5.4 [kW]. We then chose the fuel flow for the tubular

Fig. 3 (a) Fuel and air channels, PEN structure, and injection tube temperature along the cell length. (b) Fuel channel compo-nent mole fraction along the cell length.

Fig. 4 (a) Comparison between predicted and measured voltage-current densitycharacteristics. An experimental data of a tubular Siemens Westinghouse SOFCpresented in Ref. [1] has been used for the fuel cell model verification. (b) The pre-dicted cell power versus current density profile.



SOFC model to meet the average current density and 85% fuelutilization requirements. In addition, the tubular system is knownfor operating with lower air excess ratios due to the ability of thetubes in tolerating thermal gradients [14]. Hence, a relatively lowair excess of four was chosen for the SOFC operation. The keycell operation variables at the design point are summarized inTable 4.

4 Modeling and Integration of SOFC/GT System

This section describes the modeling work on the turbomachi-nery part of the two SOFC/GT hybrid systems in single- anddual-shaft configurations. The SOFC nominal operating condi-tions shown in Table 4 are used as a baseline model for the sizingof gas turbines to match the SOFC design.

4.1 Single-Shaft GT. The GT model incorporates the shaftrotational speed dynamics, the compressor and the turbine sub-models. The performance data used in this study is specified in theform of compressor and turbine maps [15], which present absolutevalues for a specific compressor. Since no map of commerciallyavailable turbines matched the specifications of the mass flow andpressure ratios required by the SOFC/GT under investigation, themaps used in this modeling work, shown in Fig. 5, were derivedby normalization and proper scaling. The main variables used inthose models include pressure p, flow _m, temperature T and powerP. Note that the subscripts denote the component (c for compressorand t for turbine) and the inlet or outlet (1 or 2, respectively). Forexample, pc2 denotes the outlet temperature of the compressor.

These compressor and turbine maps provide steady-state massflow, pressure ratio, and efficiency as a function of turbine rota-tional speed. The mass flow can be calculated from the perform-ance maps for any given rotational speed, pressure ratio. Once themass flow is determined, a compressor efficiency can be deter-mined from the efficiency map. Knowing the isentropic efficiency,the compressor exit temperature can be determined from the isen-tropic relations described as follows:

TC2 ¼ TC1 1þ 1

gcomp

pc2pc1

� �c�1c �1

24

35

8<:

9=; (6)

The power Pc required to drive the compressor can be related tothe mass flow rate _mc and the enthalpy change across the compres-sor from the first law of thermodynamics as

Pc ¼ _mcðhc2 � hc1Þ (7)

Assuming that the specific heat coefficients of air do not change,we have

Pc ¼ _mccpjcðTc2 � Tc1Þ (8)

The turbine model is constructed in a similar way as the compres-sor. The turbine/generator rotational dynamics are determined by

the power generated by the turbine, Pt, the power required to drivethe compressor Pc and the power drawn by the generator Pgen as:

dN

dt¼ Ptgm � Pc � Pgen

a � N � J (9)

Where N is the turbine speed in rpm and gm is the turbine mechan-ical efficiency that accounts for energy losses due to friction. Theturbocharger inertia is considered constant and equal to a typicalvalue of 0.95. The turbocharger inertia J is the sum of rotor iner-tia, compressor inertia and turbine wheel inertia about the axis ofrotation. The factor a¼ (2p/60)2 is a result of converting the speedfrom rad/s to revolutions per minute (rpm).

In addition, in modeling the catalytic burner (CB), the mass/temperature dynamics used in Ref. [9] are taken into account asfollows:

dmcb

dt¼ Wca þWan �Wt; (10)

mcbcp;cbdTcbdt

¼Xnk¼1

NInk;cbh

Ink;cb �

Xnk¼1

NOutk;cbh

Outk;cb (11)

where Wca, Wan are the anode and cathode outlet mass flows,respectively, and Wt is the flow through the turbine. hInk;cb; h

Outk;cb are

the inlet and outlet enthalpies of the gas species k and NInk;cb;N

Outk;cb

are the associated molar inflow and outflow rates.

4.2 Dual-Shaft GT. The model for the dual shaft system isdeveloped following the same modeling guidelines used for thesingle- shaft design. The dual-shaft turbine maps are resized prop-erly so that the dual-shaft turbine power matches that of the sin-gle-shaft system at the design point. The same equations are usedto calculate the inlet/outlet temperatures and enthalpies for thetwin-shaft GT modeling. The rotor dynamics of gas and powerturbines are modeled as in Eqs. (12) and (13), respectively,

dN1

dt¼ Pt;1gm;1 � Pc

a � N1 � J1 (12)

dN2

dt¼ Pt;2 � bN2

2 � Pgen

a � N2 � J2 (13)

where b is the friction coefficient of the power turbine. Contraryto Eq. (12), the damping effect due to the mechanical friction isrepresented in a separate form (bN2

2) which yields a stable dampedresponse of the power turbine. Since these two turbines have nomechanical coupling, the design offers flexibility in operating thecompressor and the generator at different speed to achieve optimalefficiency.

5 Steady-State Performance Evaluation

In this section, we first calculate the steady state operationregimes for the two different design options. Three control varia-bles are varied independently within their respective limits. Eachcombination determines an output power and an operation pointof the system.

5.1 Operation Envelopes. Figure 6 show the steady-stateoperation ranges for a single- and dual-shaft SOFC/GT hybridmodel, respectively. Steady state operation exists only in the dark-shaded areas. The power ranges of two designs are very close:3.0– 6.0kW for the single-shaft design and 3.0–5.7kW for thedual-shaft design. This is because the SOFC has been built upunder the same design condition and the turbines have been mod-eled to produce a similar power at the 100% rpm for the compari-son study purpose. For the single shaft system, the efficiencyvaries from 32.0% to 42.6%, while for the dual shaft, a narrowerrange of efficiency window is observed for its entire operating

Table 4 Design point data of the tubular SOFC

Parameter Value Comments

Cell Power 90 [W] Single Cell Power: 90[W]Cell Number: 60

Total Stack Power: 5.4 [kW]Voltage 0.67 [V]Current Density 2000 [A/m2]FU 85%Air excess ratio 4Fuel flow 0.099 [kg/sec] 0.002 [mol/sec]Air flow 0.44 [kg/sec] 0.012 [mol/sec]



range, namely, from the lowest 32.0% to the highest 39.2%. Thedual-shaft hybrid system show slightly better part-load performancethan the single-shaft system does. The efficiency values are plottedalong the boundary lines of the operation regimes depicted inFig. 6. The efficiencies are higher in the lower boundary points ofthe turbine power (PTurb) and the shaft speed (N) while the low effi-ciencies are found in the lower boundaries of the SOFC temperature(TCELL) and the generator load (PGEN). For the high fuel flow andlow PGEN combination, which is outside the shaded area on the lowefficiency side, the turbine speed is steadily climbing far beyond theoperating ranges (overspeed) and the fuel cell is also over cooledand therefore the voltage is expected to be low. On the other hand,the cause of infeasible operation related to the other extreme end(low fuel flow, high PGEN) is due to the fuel/air starvation in thefuel cell stack along with the high SOFC temperature limitation.

The single-shaft design has a wider operation range than that ofthe dual shaft as shown in the plots of Fig. 6. This is becausein the dual-shaft model, the compressor pressure ratio is shared bythe gas- and power-turbines. The decrease in the turbine power ismainly due to the less pressure ratio applied to one stage in thedual-shaft configuration. Besides, the single-shaft design has ahigher power split ratio (PGEN/PNET) compared with the dual-shaftdesign. Figure 7 shows that a power split ratio for the single-shaftdesign varies over 7%–8% while that of a dual-shaft design isnearly 2%. The reduced turbine power generation range in thedual-shaft model leads to the decrease in the power split ratio. Indual-shaft design, the lower/upper boundaries of PGEN are almostflat over the entire PNET region. In contrast, the upper boundary ofthe PGEN in the single-shaft design decreases by more than 50%from the maximum PGEN. This means that the small(large) gener-ator load variation is expected for the dual(single)-shaft design,when a load is changed along the high efficiency boundary line.

Given the large thermal time constant and the delicacy of theSOFC units, it might be desirable to keep the SOFC at a constantoperating condition even when the load demand has beenchanged. Figure 8 presents the load operation range while a con-stant SOFC output power is maintained. The load variation over afixed SOFC power is very limited (6 0.3kW) and uniform overthe entire PNET range for both single- and dual-shaft cycles. Thisanalysis shows that using SOFC as the base power plant and thegenerator for load following is not a feasible strategy for this classof SOFC/GT system.

SOFC cell temperature is another practical constraint, as itaffects reliability and lifetime of the cell, as well as the systemefficiency. Maintaining relatively high-level of SOFC temperaturecan be made possible in the high load operation regime, (e.g.,

1040K can be achieved in the region of PNET �5.0 kW in the sin-gle design and PNET �5.2 kW in the dual design as seen from Fig.6). In addition, based on the steady state performance data, operat-ing the system at a constant SOFC temperature for different loadcondition seems feasible for certain load operation range. Thelargest load operation range for which the PNET can vary while thetemperature is kept constant is found between 4.0–5.5 kW inthe single-shaft design, see the upper plot in Fig. 9. However, forthe dual shaft counterpart, this range becomes narrower and isalmost constant regardless the load condition (see the lower plotin Fig. 9), which indicates that a single shaft design is more favor-able for the part-load operation under a constant SOFC tempera-ture constraint. It is also noticeable that maintaining a constantshaft speed is doable over the entire load interval for both thesingle- and dual-shaft designs.

5.2 Analysis of Part-Load Operation. In this section, thesystem part-load behavior is investigated. The strategies for part-load operation and for effective transition from one operationpoint to another are discussed.

5.2.1 Single-Shaft SOFC/GT Design. The operation of SOFC/GT plants is dictated by three different control inputs, namely thefuel flow, the SOFC current density, and the generator power.Therefore, there exist multiple ways of achieving a prescribed loadfollowing objective. This study investigates load change schemesto explore the control design space that can achieve fast and safeload following operation. To illustrate the concept and the analysismethod, we consider two load points with PNET¼PA andPNET¼PB. By analyzing the feasible input regimes for each oper-ating point and the overlap in the two corresponding regions, wegain insight on how to achieve efficient part load operation whilefacilitating fast load following. As a representative example, thefeasible input setpoints matching the powers of 5.0kW (PA) and5.7kW (PB) are calculated as displayed in Fig. 10 for the single-shaft design. The crucial system variables such as the fuel cell tem-perature, system efficiency, and the shaft speed are shown in theoperating area. The areas highlighted in Fig. 10(b)–10(d) indicatethat the combination of the corresponding inputs can generate thespecified powers. The white area represents input points thatcannot meet the power demand. Major observations and findingsconcerning the load operation are summarized as follows:

Regions of feasible control inputs: It is clear that as PNET

increases from lower power (5.0 kW) to a higher power (5.7 kW),the entire operating regime shifts in the fuel flow WFuel and theSOFC current density (ICOM) plane such that more power from the

Fig. 5 Normalized performance map for a compressor. It is based on a generic map from Ref. [15].



fuel cell stack can be produced. This is the case with both single-and dual-shaft designs. Note that at a constant net power, the effi-ciency is inversely proportional to the fuel flow since g¼PNET/(WFuel �LHV) and thus the corresponding fuel flows at the power

of 5.0 kW and 5.7 kW can be readily calculated from the effi-ciency data of Fig. 10(b) for the entire feasible operating range.Note that the diagonal distribution of the feasible region is due tothe fact that PNET¼PFUEL (Icom)þPGEN. Outside this region, ei-ther too much (upper right area) or not enough (lower left) powerwill be produced.

Sensitivity of part load efficiency to control variables: FromFig. 10(b), it is observed that high efficiency setpoints are locatedin the upper boundary of the operating regime while low effi-ciency setpoints are situated in the lower boundary line. The set-points associated with g¼ 39% for the 5.0 kW power are spreadout most widely along the operation regimes and the range of thefeasible operation is shrinking as g increases. In particular, PGEN

increases while ICOM tends to decrease as g reaches its maximumof 41%. The reduction in ICOM can be attributed to the fact thatthe low fuel supply increases the chance of the fuel starvationin the fuel channel and thus limiting the operating range of ICOM.On the other hand, in case an excessive fuel flow enters the fuelcell stack, the gas turbine overspeeding can occur. Note that thelowest efficiency points are positioned where PGEN value is near

Fig. 6 Steady-state operating regimes of a single (LHS) and dual-shaft (RHS) SOFC/GT cycle: Turbine power, shaft speed, fuelcell temperature, and generator load. The efficiency data are plotted along the upper and lower boundaries of the feasible oper-ating region.

Fig. 7 Comparison of power split ratios for single- and dual-shaft designs



to zero and the SOFC current values are relatively high. In sum-mary, the high efficiency of the hybrid system under study can beachieved if the operation can be sustained under a low fuel flow, alow fuel cell current, and a high generator load. In other words,maximizing the power split ratio PGEN/PNET under the constraintof PNET¼PFUEL(ICOM)þPGEN is the way of achieving the highefficient operation. This observation reveals the fact that the selec-tion of PGEN as a control variable cannot only expand the operat-ing region, but also make significant contribution to achieve ahigh efficiency of the SOFC/GT hybrid system.

Temperature and turbine speed variation analysis: From the per-formance maps in Fig. 10(c), the fuel cell temperature tends toincrease when the generator load and the SOFC current are set tobe high and the fuel flow to be low. In this control setting, moreheat is generated from the electrochemical process and the less aircooling effect is applied to the fuel cell. The operating domains ofthe fuel cell temperature for the set powers of 5.0 kW and 5.7 kWare computed to be [1002,1020]deg K and [1025,1048]deg K,respectively. This means that with the load change from 5.0 kW to5.7 kW, maintaining constant cell temperature is not likely to hap-pen. However, minimizing the fuel cell temperature variation canbe achieved by well coordinated input combinations. In this partic-ular example, the setpoints from (g,ICOM,PGEN)¼ (39.5,1750,350)at 5.0 kW to (38.9,2100,300) at 5.7 kW leads to the smallest fuelcell temperature variation of 5 K. It is also noticeable that in caseof a load increase operation, keeping constant fuel cell temperatureand achieving high efficiency are competing requirements, the celltemperature deviation can be minimized at the cost of the systemefficiency. However, in case of load decrease scenario, the two-foldpurpose to achieve the high efficiency and minimal fuel cell tem-perature change is achievable. It should be noted that the resultdepends on both the magnitude and direction of load change. Theshaft speed varies uniformly over an interval of [2.57,3.59]� 105rpm for the power of 5.0 kW and [2.60,2.84]� 105rpm for thepower of 5.7 kW, indicating that part-load operation with a constantspeed is possible. However, varying the speed of the gas turbinecan provide greater flexibility in turbine operation.

5.2.2 Dual-Shaft SOFC/GT Design. The performance analy-sis for a dual-shaft SOFC/GT cycle has been also conducted withrespect to the performance critical factors, such as the fuel celltemperature and the efficiency, and the results are shown in Fig.11. The plots show the feasible setpoints of the efficiency (Fig.11(a)) and fuel cell temperature (Fig. 11(b)) for two output powerlevel of 5.0kW and 5.7kW, respectively. It is shown that the cur-rent density and the fuel flow increase as the power level increasesfrom 5.0kW to 5.7kW (refer to Table 5 for the fuel flow varia-tion). The fuel cell temperature is also increased since more heatis generated at the high power of 5.7kW. Even though the two-shaft design of the hybrid SOFC/GT cycle is advantageous in me-chanical design because of its simplicity, the operating range isconsiderably smaller in comparison to the single-shaft configura-tion as shown in Fig. 11. The load change from 5.0kW to 5.7kWin the dual shaft configuration leads to less changes in the fuel celltemperature and the turbine shaft speed than the single-shaft con-figuration. For example, the efficiency gap between 5.0kW and5.7kW in the dual shaft design is only 0.8% compared to 3.3% inthe single-shaft design, the temperature gap is 10 K less in com-parison to the single-shaft cycle. Due to the low power split ratio,the variable speed in the dual-shaft design exhibits the uniformpart load efficiency.

Table 5 compares the admissible ranges of the three independ-ent control variables at the two different power levels. The opera-tion windows associated with the fuel flow and the SOFC currentdensity at 5.0kW and 5.7kW are completely separated, while thereis much overlap among the feasible intervals of the generator loadfor both single- and dual-shaft systems.

As shown in Fig. 10, under a constant fuel flow (see g¼ 41% at5.0kW in Fig. 10), the temperature increases as the fuel cell cur-rent (generator load) increases (decreases). This suggests thatbetween the two competing factors, namely (a) increase in SOFCcurrent increases the temperature and (b) decrease in generatorload decreases the temperature, the former is more dominant.However, the generator load shows a very attractive feature that itcan exert constant influence on the SOFC temperature at the dif-ferent power levels. For example, the temperature differencesattributed to the generator load variations in the middle value of

Fig. 8 Operating envelope with SOFC power constraints: Sin-gle-shaft (upper plot) and dual-shaft (lower plot). The numberson the plots indicate the output power of the SOFC.

Fig. 9 Operating envelope with temperature constraints:Single-shaft (upper plot) and dual-shaft (lower plot). The num-bers shown on the plots are cell temperature TCELL in deg K.



an SOFC current are 14 K at the power of 5.0 kW and 13 K at thepower level of 5.7 kW. Hence, in case the SOFC current and fuelflow are designated as controlling variables for the power controlobjective as claimed by Ref. [14], the generator load can be uti-lized as an alternative control element for an SOFC temperature

management.

6 Dynamic Performance Evaluation

It has been established that the hybrid SOFC/GT system is sus-ceptible to shutdown when a sudden load increase is applied [9].In this analysis, we use the operating envelope identified earlier tocharacterize the shutdown mechanism for two different SOFC/GTconfigurations. The region of attraction (ROA), a notion used to

Fig. 10 The single-shaft operating regime to produce the net powers of 5.0kW and 5.7kW.(a),(b) system efficiency 3D/2D maps, (c) fuel cell temperature variation at 1000 K, (d) shaftspeed (x 105) as functions of SOFC current density and a generator load.



characterize the stability of a nonlinear system is used in this pa-per to elucidate the stability properties of the SOFC/GT. For agiven operating point and associated equilibrium, the ROA isdefined as the set of all initial states from which the trajectorieswill converge to the steady state equilibrium point.

6.1 Shutdown Problem. In this section, the ROAs of twoSOFC/GT models are identified and analyzed for the shutdownphenomenon. We denote xss(PNET) and ROA(PNET) as the steadystate and region of attraction respectively for a given powerdemand PNET. Then the ROA provides a numerical tool to cap-ture and understand the shutdown phenomenon. For example,consider the case that the system is settled at an equilibrium pointxss(PA), but it is required to step up the power to PB with PA<PB,the system will shutdown if

xssðPAÞ 62 ROAðPBÞ (14)

On the other hand if

xssðPAÞ 2 ROAðPBÞ (15)

the system can reach the new desired equilibriumThe ROAs are computed in terms of three dominant states,

namely the fuel cell temperature, the CB mass, and the shaftspeed, as investigated in the previous study [9]. The three dimen-sional region of attraction corresponding to PNET¼ 5.7kW withinput settings (WFueL,ICOM,PGEN)¼ (0.002,2100,390) is sketchedon two dimensional planes (with the cell temperature and CBmass as two axes) as the shaded areas in Fig. 12 for four differentshaft speeds. From the region of attraction boundaries it can be

seen that if the initial condition for the mass and the rotationalspeed is high, then the required initial condition for the tempera-ture is lowered. This trend can be explained by noting that thehigher the initial temperature, mass, and rotational speed are, thehigher turbine power is. The energy provided to the GT shaftincreases as temperature, mass and rotational speed increase.Thus; for example, to reach the stable equilibrium starting at lowmass, low rotational speed and PNET¼ 5.7kW, the temperaturehas to be high in order to make up for the energy needed to sup-port the load on the GT shaft.

To illustrate a situation when system shutdown occurs, threeload operation scenarios are evaluated in the single-shaft SOFC/GT system as shown in Table 6. S1, S3, S4 are operation pointswith the highest efficiency for their specified powers of 4.6/5.0/5.7 kW while S2 is the lowest efficiency point at the power of4.6 kW. In case of a small step load change from 5.0kW(S3) to5.7 kW(S4), it can be shown that the equilibrium point of5.0 kW(S3) resides within the ROA of 5.7kW with a large marginto the lower boundary line. On the other hand, consider two larger

Fig. 11 The dual-shaft operating regime to produce the net powers of 5.0kW and 5.7kW. (a) sys-tem efficiency, (b) fuel cell temperature as functions of a generator load and a SOFC currentdensity.

Table 5 The control variables’ distribution matching the netpowers of 5.0 kW and 5.7 kW

Turbine type Input 5.0 kW 5.7 kW

Single WFuel [1.7, 1.95]�10�3 [2,2.1]�10�3

ICOM [1679,1909] [1955,2185]Pgen [0,420] [120,480]

Dual WFuel [1.6, 1.65]�10�3 1.8�10�3

Icom [1700, 1750] 2000Pgen [0, 150] 25



step load maneuvers from 4.6kW(S1;S2) to 5.7(S4). Note that S1and S2 differ in that S1 is optimized for efficiency while S2 is not.The equilibrium point with 4.6kW(S1) falls slightly outside of theROA of 5.7kW as shown in Table 6(65%rpm) while that of S2 islocated above the lower boundary of the ROA. This means thatthe load change from 4.6kW(S1) to 5.7kW(S4) leads the system toshutdown while the other two operations, namely S2 ! S4 andS3 ! S4 transient are sustainable.

The analysis can be validated by the simulation when thedemanded load power steps, from Pnet¼ 4.6/5.0kW toPnet¼ 5.7kW, are applied without feedback control. The input set-tings, identified from the previous section, are used to change thefuel flow, the current, and the generator power as listed in Table6. It is observed that the system shuts down after the steps areapplied from 4.6kW(S1) to 5.7kW(S4) at t¼ 2000sec. During the

4.6kW(S1) to 5.7kW(S4) step, the immediate increase in the gener-ator load deprives the turbine from having enough power to sup-ply the air during the transient to support SOFC operation,causing the turbine shaft to stall and eventually the system to shutdown. On the contrary, when a load switches from 4.6(S2) or5.0(S3) to 5.7kW(S4), the system shutdown does not occur due tothe sufficient initial kinetic energy in the turbine and thermalenergy in the SOFC exhaust.

A dual-shaft gas turbine design has been also studied to examinethe operating characteristics and the load following performance fora SOFC/GT. We consider an open-loop response when a net powerswitches from 4.6kW(JD1)/5.0kW(D2) to 5.7kW(D3) which is thesame load change conditions as those used in the single-shaft modelanalysis. The corresponding input settings are (WFUEL, ICOM,PGEN)¼ (0.00175,1750,100)D1, (0.00185,1850,100)D1, and (0.0021,2000,50)D3, which offer the highest efficiency set points at thepowers of 4.6/5.0/5.7kW, respectively. Figure 14 depicts that both

Fig. 12 ROA sketch for a single-shaft SOFC/GT model with anet power of 5.7kW and input setting (WFuel,ICOM,PGEN)5(0.002,2100,390). The ROA of a SOFC temperature and a CBmass are computed under four different initial turbine shaftspeeds. The equilibrium point is (rpm,TCELL,mCB)5 (65% rpm,1039 �C, 0.117kg).

Fig. 13 Load step response of a single shaft SOFC/GT systemfrom 4.7 kW TO 5.7 kW under highest (S1, S3, S4)/lowest S2 effi-ciency setpoints for current density, fuel, and generator load asa function of load

Table 6 The load operation points to illustrate the shutdownbehavior of single- and dual-shaft SOFC/GT systems. Note:Input5 [WFuel (kg/s), Icom (A/m2), PGEN (W)], State5 [rpm(%),Tcell(deg K),mCB (kg)]

PNET Single

4.6 kW S!Input: (0.0016,1800,200)S!State: (65,1016,0.127)S2!Input: (0.0019,1750,0)S2!State: (90,1002,0.151)

5.0 kW S3!Input: (0.0017,1900,350)S3!State: (60,1038,0.124)

5.7 kW S4 !Input: (0.002,2100,390)S4 !State: (65,1039,0.117)

PNET Dual4.6 kW D1!Input: (0.00175,1750,100)

D1!State: (65,1014,0.147)

5.0 kW D2!Input: (0.00185,1850,100)D2!State: (67,1017,0.148)

5.7 kW D3!Input: (0.0021,2000,50)D3!State: (67.0,1042,0.153)

Fig. 14 ROA lower boundary for a dual-shaft SOFC/GT modelfor PNET5 5.7kW and (WFuel,ICOM,PGEN)5 (0.0021,2000,50). Theequilibrium point is (rpm,TCELL,mCB)5 (67% rpm, 1042 �C,0.15kg).



equilibrium points of 4.6kW(D1) and 5.0kW(D2) are contained in theROA at the power of 5.7kW(D3). Therefore, no shutdown isobserved in Fig. 15. In contrast to the single-shaft load change caseof 4.6kW! 5.7kW, one can notice that the small amount of the gen-erator power (50W) is applied due to the low power split ratio andthereby the dual-shaft SOFC/GT becomes less vulnerable to the sys-tem shutdown under aggressive load change.

7 Conclusions

This study has examined the characteristics of the SOFC/GThybrid cycles from the fundamental operating regime to the partload performance. Two different mechanical designs are assumed:dual shaft and single shaft as the compressor turbine connectionmechanism. The analysis leads to the following conclusions: First,the single-shaft design provides wide operation envelopes com-pared to the dual shaft operation when the same compressormodel is employed in the SOFC/GT system. The gap between theoperation ranges stems from their mechanical designs, as the com-pressor discharge pressure in a dual-shaft design has to be sharedby two turbines of a turbocharger and thus the power split ratio ofthe dual shaft SOFC/GT becomes much smaller than that of thesingle-shaft design. The dual shaft cycle would require a highercompressor pressure ratio to achieve the operating envelope to becomparable to the conventional single-shaft design. Furthermore,the system efficiency is less sensitive to the load in part load oper-ation in the dual shaft design in comparison to the single-shaftcycle. Second, turbine shaft speed control through a generatorload manipulation in both SOFC/GT configurations can be effec-tive in enhancing the part load efficiency and maintaining the fuelcell temperature variation at its minimal. However, its usefulnessis more pronounced in a single-shaft design. Third, through modelbased simulations, it was demonstrated that the optimal steadystate setpoints lie on the boundary of the admissible operationregion and thus the use of optimal steady state setpoints for loadtransitions makes the system susceptible to transient issues andimposes the need for advanced control schemes. By analyzing theregion of attraction, the responses to the load change of the dual-shaft model has been proved to be more robust against the shut-down problem than its single-shaft counterpart. The dynamic loadresponse could be further improved by using more advancedmodel-based controllers. This is a part of ongoing research.

Acknowledgment

This work is funded in part by U.S. Army TARDEC and in partby U.S. Navy under NEEC (Naval Engineering Education Center).

NomenclatureC(�) ¼ concentration of species (�) (mol/m3)cP ¼ heat capacity (J/kg�K)df/a ¼ hydraulic diameter of the fuel/air channelF ¼ Faraday’s constant (C/mol)

h(�) ¼ gas enthalpy of species (�) (J/kg)I ¼ shaft inertia (kg m2)

ICOM ¼ current density (A/m2)L ¼ cell length (cm)m ¼ mass (kg)N ¼ shaft rotational speed (rpm)

Nin/out,i ¼ inlet/outlet molar rate of species i (mol/s)NU,i ¼ Nusselt number of channel ip(�) ¼ pressure of (�) (Pa)P(�) ¼ power of (�) (kW)

rSR/WGS/Ox ¼ rate of reaction (mol/s�m [2])~R ¼ universal gas constant (J/K�mole)

ROhm ¼ cell resistance (X � m2)sp, ¼ cell pitch/2T ¼ temperature (K)U ¼ voltage (V)V ¼ volume (m3)_m ¼ flow (kg/s)

ePEN/INJ ¼ PEN/injector emissivitykPEN ¼ PEN thermal conductivity (J/m � s � K)kair ¼ air ratiovs,. ¼ stoichiometric coefficient of species s

qPEN/INJ ¼ PEN/injector density (kgm�3)r ¼ Stefan-Boltzmann constant (W/m2 � K4)

rAn ¼ anode electrical conductivity (1/X � m)sAn/El/Ca ¼ anode/electrolyte/cathode thickness (m)

References[1] Singhal, S. C., and Kendall, K., 2003, High Temperature Solid Oxide Fuel

Cells, Elsevier, New York.[2] Campanari, S., 1998, “Power Plants Based on Solid Oxide Fuel Cells Combined

With Gas Turbine Cycles,” Ph.D. dissertation, Polytechnic University of Milan,Milan, Italy.

[3] Larminie, J., and Dicks, A., 2004, Fuel Cell System Explained, Wiley, New York.[4] Palsson, A., Selimovic, A., and Sjunnesson, L., 2000, “Combined Solid Oxide

Fuel Cell and Gas Turbine Systems for Efficient Power and Heat Generation,”J. Power Sources, 86, pp. 442–448.

[5] Roberts, R. A., and Brouwer, J., 2006, “Dynamic Simulation of a Pressurized220kW Solid Oxide Fuel-Cell Gas- Turbine Hybrid System: Modeled Perform-ance Compared to Measured Results,” J. Power Sources 3, pp. 18–25.

[6] Roberts, R. A., Brouwer, J., Jabbari, F., Junker, T., and Ghezel-Ayagh, H.,2006, “Control Design of an Atmospheric Solid Oxide Fuel Cell/Gas TurbineHybrid System: Variable Versus Fixed Speed Gas Turbine Operation,” J. PowerSources 161, pp. 484–491.

[7] Wang, X., Huang, B., and Chen, T., 2007, “Data-Driven Predictive Control forSolid Oxide Fuel Cells,” J. Process Control 17, pp. 103–114.

[8] Wchter, C., Lunderstdt, R., and Joos, F., 2006, “Dynamic Model of a Pressur-ized SOFC/Gas Turbine Hybrid Power Plant for the Development of ControlConcepts,” J. Fuel Cell Sci. Technol., 3, pp. 271–279.

[9] Tsourapas, V., 2007, “Control Analysis of Integrated Fuel Cell Systems with EnergyRecuperation Devices,” Ph.D. thesis, University of Michigan.

[10] Oh, S.-R., and Sun, J., 2010, “Optimization and Load-Following Characteristicsof 5kw-Class Tubular Solid Oxide Fuel Cell/Gas Turbine Hybrid Systems,”American Control Conference, Baltimore, MD, pp. 417–422.

[11] Xi, H., 2007, “Dynamic Modeling and Control of Planar SOFC Power Sys-tems,” Ph.D. thesis, University of Michigan.

[12] Aguiar, P., Adjiman, C. S., and Brandon, N. P., 2004, “Anode-SupportedIntermediate Temperature Direct Internal Reforming Solid Oxide Fuel Cell. I:Model-Based Steady-State Performance,” J. Power Sources 138, pp. 120–136.

[13] Hall, D. J., 1997, “Transient Modeling and Simulation of a Solid Oxide FuelCell,” Ph.D. dissertation, University of Pittsburgh, PA.

[14] Stiller, C., Thorud, B., Seljebo, S., Mathisen, O., Karoliussen, H., and Bolland,O., 2005, “Finite-Volume Modeling and Hybrid-Cycle Performance of Planarand Tubular Solid Oxide Fuel Cells,” J. Power Sources 141, pp. 227240.

[15] Stiller, C., Thorud, B., and Bolland, O., 2005, “Safe Dynamic Operation of aSimple SOFC/GT Hybrid System,” Proceedings of the 2005 ASME TurboExpo, Reno, NV.

Fig. 15 System responses of a dual shaft SOFC/GT during astep from 4.6kW to 5.7kW, namely D1 ! D3 and D2! D3. Thesame conditions as the single-shaft model simulation havebeen used.



Date post:	08-Mar-2018
Category:	Documents
Upload:	hathu
View:	212 times
Download:	0 times

Performance Evaluation of Solid Oxide Fuel Cell Engines Integrated With Single/ Dual...

Documents